Solve for $t$. Give an exact answer. $3t-18=4\left(-3-\dfrac34t\right)$ $t =$
Answer: We need to manipulate the equation to get $t $ by itself. $\begin{aligned} 3t-18 &= 4\left(-3-\dfrac34t\right) \\\\ 3t-18 &= -12-3t~~~~~~~~~~\gray{\text{Distribute}}\\\\ 3t-18{+3t} &= -12-3t{+3t} ~~~~~~~~~~\gray{\text{Add 3t to each side}}\\\\ 6t-18 &=-12 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 6t-18{+18} &= -12{+18} ~~~~~~~~~~\gray{\text{Add 18 to each side}}\\\\ 6t &= 6~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{6t}{{6}}&= \dfrac{6}{{6}}~~~~~~~~~~\gray{\text{Divide each side by 6}} \\\\ t &= {1} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $t = { 1 }~~~~~~~~$ [Let's check our work!]